Simulated conformality of atomic layer deposition in lateral channels: the impact of the Knudsen number on the saturation profile characteristics

Atomic layer deposition (ALD) is exceptionally suitable for coating complex three-dimensional structures with conformal thin films. Studies of ALD conformality in high-aspect-ratio (HAR) features typically assume free molecular flow conditions with Knudsen diffusion. However, the free molecular flow assumption might not be valid for real ALD processes. This work maps the evolution of the saturation profile characteristics in lateral high-aspect-ratio (LHAR) channels through simulations using a diffusion-reaction model for various diffusion regimes with a wide range of Knudsen numbers (10^6 to 10^{-6}), from free molecular flow (Knudsen diffusion) through the transition regime to continuum flow conditions (molecular diffusion). Simulations are run for ALD reactant partial pressures spanning several orders of magnitude with the exposure time kept constant (by varying the total exposure) and with the total exposure kept constant (by varying the exposure time). In a free molecular flow, for a constant total exposure, the saturation profile characteristics are identical regardless of the LHAR channel height and the partial pressure of the reactant. Under transition regime and continuum conditions, the penetration depth decreases and the steepness of the adsorption front increases with decreasing Knudsen number. The effect of varying individual parameters on the saturation profile characteristics in some cases depends on the diffusion regime. An empirical "extended slope method" is proposed to relate the sticking coefficient to the saturation profile's characteristic slope for any Knudsen number.